.. note::
    :class: sphx-glr-download-link-note

    Click :ref:`here <sphx_glr_download_intro_scipy_auto_examples_plot_2d_minimization.py>` to download the full example code
.. rst-class:: sphx-glr-example-title

.. _sphx_glr_intro_scipy_auto_examples_plot_2d_minimization.py:


=========================================
Optimization of a two-parameter function
=========================================




.. code-block:: python


    import numpy as np


    # Define the function that we are interested in
    def sixhump(x):
        return ((4 - 2.1*x[0]**2 + x[0]**4 / 3.) * x[0]**2 + x[0] * x[1]
                + (-4 + 4*x[1]**2) * x[1] **2)

    # Make a grid to evaluate the function (for plotting)
    x = np.linspace(-2, 2)
    y = np.linspace(-1, 1)
    xg, yg = np.meshgrid(x, y)







A 2D image plot of the function
###########################################################
 Simple visualization in 2D



.. code-block:: python

    import matplotlib.pyplot as plt
    plt.figure()
    plt.imshow(sixhump([xg, yg]), extent=[-2, 2, -1, 1], origin="lower")
    plt.colorbar()




.. image:: /intro/scipy/auto_examples/images/sphx_glr_plot_2d_minimization_001.png
    :class: sphx-glr-single-img




A 3D surface plot of the function
###########################################################



.. code-block:: python

    from mpl_toolkits.mplot3d import Axes3D
    fig = plt.figure()
    ax = fig.add_subplot(111, projection='3d')
    surf = ax.plot_surface(xg, yg, sixhump([xg, yg]), rstride=1, cstride=1,
                           cmap=plt.cm.jet, linewidth=0, antialiased=False)

    ax.set_xlabel('x')
    ax.set_ylabel('y')
    ax.set_zlabel('f(x, y)')
    ax.set_title('Six-hump Camelback function')




.. image:: /intro/scipy/auto_examples/images/sphx_glr_plot_2d_minimization_002.png
    :class: sphx-glr-single-img




Find the minima
###########################################################



.. code-block:: python

    from scipy import optimize

    x_min = optimize.minimize(sixhump, x0=[0, 0])

    plt.figure()
    # Show the function in 2D
    plt.imshow(sixhump([xg, yg]), extent=[-2, 2, -1, 1], origin="lower")
    plt.colorbar()
    # And the minimum that we've found:
    plt.scatter(x_min.x[0], x_min.x[1])

    plt.show()




.. image:: /intro/scipy/auto_examples/images/sphx_glr_plot_2d_minimization_003.png
    :class: sphx-glr-single-img




**Total running time of the script:** ( 0 minutes  0.146 seconds)


.. _sphx_glr_download_intro_scipy_auto_examples_plot_2d_minimization.py:


.. only :: html

 .. container:: sphx-glr-footer
    :class: sphx-glr-footer-example



  .. container:: sphx-glr-download

     :download:`Download Python source code: plot_2d_minimization.py <plot_2d_minimization.py>`



  .. container:: sphx-glr-download

     :download:`Download Jupyter notebook: plot_2d_minimization.ipynb <plot_2d_minimization.ipynb>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.readthedocs.io>`_